SPECTRAL METHODS FOR MODELING AND ESTIMATING VIBRATION FATIGUE DAMAGE IN ELECTRONIC INTERCONNECTS

Abstract

The purpose of this thesis is to explore the accuracy of fatigue damage estimation in printedwiring assembly (PWA) interconnects, using purely frequency-domain (also known as spectral) information such as the power spectral density (PSD) of the input excitation. The test case used in this study is the estimation of fatigue damage accumulation rate in the critical interconnects of low profile quad flat-pack (LQFP) components on a PWA, under broad-band random vibration excitation. this study examines whether the fatigue predictions made with this frequency-domain approach are consistent with those obtained from a direct time-domain approach. The frequency-domain response modeling is achieved using a two-stage global-local modeling process using a finite element model (in ABAQUS©), where the dominant modal participation factors for the dynamic response is obtained using a dynamic global simplified dynamic finite element model consisting of shell elements to represent the entire PWA. The PSD of the input excitation is applied as a boundary condition and the PSD of the PWA strain response is recorded at the base of critical components. The corresponding PSD for the dynamic strain response at critical interconnects is estimated with strain-transfer functions (STFs) for each dominant mode, obtained from detailed 3D quasi-static nonlinear local models of the component, adjacent PWB, and the interconnects. The global-local STF provides a relationship between the level of equivalent strain in the critical interconnects and the flexural strain at the adjacent surface of the PWB. The STF for each of the dominant vibration modes is obtained by imposing the corresponding mode-shape predicted by the dynamic global model on the PWB, in the quasistatic local model, using multi-point constraint equations. The PSD of the equivalent strain in the critical interconnect is then estimated via linear modal superposition. A deterministic estimate of the cyclic fatigue damage accumulation rate in the critical interconnect is then conducted with the Basquin high cycle fatigue (HCF) model and linear damage superposition approach, by using three different spectral approaches for representing the strain severity with estimated probability density functions (PDFs). The three approaches include: (i) Raleigh method; (ii) Dirlik method and (iii) Range distribution function created with the Rainflow cycle counting method. Methods (ii) and (iii) are derived from a pseudo time-history created with an inverse Fourier transform. These frequency-domain results are compared to corresponding fatigue damage estimates from a multi-modal time-domain analysis method, to assess the consistency of the two approaches.